Mohabat news agency reports that government agents "completely demolished" the cemetery in the Ghal'e-dokhtar area of Kerman province.
It follows the destruction of a church building in Kerman, also by the government agents. The building had been registered as a national monument in 2009 and was supposed to be protected and restored.
Mohammad Mehdi Afzali, head of public relations for the Cultural Heritage organisation of Kerman, was quoted as saying, "Destruction of this cemetery was conducted as part of a project by the municipality and Cultural Heritage organisation, to release lands around Ghal'e-Dokhtar and Ghal'e Ardeshir.
"After the reports and photos of this destruction were published by news services, a team of experts of the Cultural Heritage office of Kerman was sent out to the cemetery to prepare an expert report."
Mr Movahedi, Deputy Director of the General Office of Cultural Heritage of Kerman said, "The historical cemetery of Christians is located in the territory of Ghal'e-Dokhtar and as far as the territory of monuments is concerned, it is necessary for all the places located in the territory of Ghal'e-Dokhtar to receive proper attention."
Mohabat also reports ongoing damage to a historic English cemetery in Boushehr port, which was also used as a burial ground for local Armenian minorities.
Crosses have reportedly been removed from the graves.